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Heat the sugar and water over high heat in a medium-sized pot until the sugar has dissolved into the water completely, about 5 minutes. Add the balsamic vinegar, strawberries, and rhubarb and lower the heat to medium-low. Allow the mixture to simmer for 1 hour, stirring every 10 minutes, crushing the fruit pieces with the wooden spoon a bit when stirring. Then remove it from the heat and allow the compote to cool to room temperature before placing in the refrigerator to thicken.
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Meanwhile, you can begin making the rice pudding. Mix the water, sugar, and milk together in a medium-sized pot over medium heat until completely combined. Add the rice and bring the mixture to a low boil. Reduce the heat to low and allow the mixture to simmer gently for 1 hour, stirring every 5-10 minutes to keep the rice pudding from sticking to the bottom of the pan and burning, and stirring every 3 minutes during the last 20 minutes of cooking as a film will keep trying to develop on top of the pudding.
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Remove it from the heat and stir in the vanilla extract. Allow to cool for 5 minutes. Meanwhile, whisk the egg yolks in a large bowl until small bubbles appear in the yolk mixture, takes about a minute. Add the rice pudding to the egg yolks, 1 tablespoon at a time, stirring constantly with a wooden spoon, until fully incorporated.
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To serve, place the desired amount of rice pudding in a cup and spoon the desired amount of the compote over it. Stir and eat. Makes about 4-6 servings, depending on your appetite.